Wall-crossing and invariants of higher rank Joyce-Song stable pairs

2011/01/12 by Sheshmani, Artan
#Algebraic Geometry (math.AG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.1101.2252

Abstract

We introduce a higher rank analog of the Joyce-Song theory of stable pairs. Given a nonsingular projective Calabi-Yau threefold X, we define the higher rank Joyce-Song pairs given by O^r_X(-n)→ F where F is a pure coherent sheaf with one dimensional support, r>1 and n≫ 0 is a fixed integer. We equip the higher rank pairs with a Joyce-Song stability condition and compute their associated invariants using the wallcrossing techniques in the category of weakly semistable objects.

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